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--- documentation:ref:fullysymmetrize [2015/11/21 10:35]
poslavskysv created
+++ documentation:ref:fullysymmetrize [2015/11/21 12:33] (current)
@@ Line 8: / Line 8: @@
 ==== Examples ====
+----
+Symmetrize expression:
+<sxh groovy; gutter: false>
+println FullySymmetrize >> 'f_abc'.t
+</sxh>
+<sxh plain; gutter: false>
+   > (1/6)*f_{bac}+(1/6)*f_{cab}+(1/6)*f_{abc}+(1/6)*f_{bca}+(1/6)*f_{acb}+(1/6)*f_{cba}
+</sxh>
+<sxh groovy; gutter: false>
+println FullySymmetrize >> 'f_abcd*t^cd_e + f_bacd*t^dc_e + f_becd*t^dc_a'.t
+</sxh>
+<sxh plain; gutter: false>
+   > (1/3)*t^{dc}_{e}*f_{abcd}+(1/3)*t^{dc}_{a}*f_{ebcd}
+      +(1/3)*t^{dc}_{e}*f_{bacd}+(1/3)*t^{dc}_{b}*f_{aecd}
+      +(1/3)*t^{dc}_{b}*f_{eacd}+(1/3)*t^{dc}_{a}*f_{becd}
+      +(1/6)*t^{cd}_{e}*f_{abcd}+(1/6)*t^{cd}_{a}*f_{ebcd}
+      +(1/6)*t^{cd}_{e}*f_{bacd}+(1/6)*t^{cd}_{b}*f_{aecd}
+      +(1/6)*t^{cd}_{b}*f_{eacd}+(1/6)*t^{cd}_{a}*f_{becd}
+</sxh>
+----
+Symmetrize only with respect to particular indices:
+<sxh groovy; gutter: false>
+println FullySymmetrize['_ae'.si] >> 'f_abcd*t^cd_e + f_bacd*t^dc_e + f_becd*t^dc_a'.t
+</sxh>
+<sxh plain; gutter: false>
+  > f_{bacd}*t^{dc}_{e}+f_{becd}*t^{dc}_{a}+(1/2)*f_{ebcd}*t^{cd}_{a}
+       +(1/2)*f_{abcd}*t^{cd}_{e}
+</sxh>
+----
+Symmetries will be taken into account:
+<sxh groovy; gutter: false>
+setSymmetric 'f_abc'
+println FullySymmetrize >> 'f_iab*f^i_cd'.t
+</sxh>
+<sxh plain; gutter: false>
+   > (1/3)*f_{iad}*f^{i}_{bc}+(1/3)*f_{iac}*f^{i}_{bd}+(1/3)*f_{iab}*f^{i}_{cd}
+</sxh>
+====See also====
+  * Related guides: [[documentation:guide:applying_and_manipulating_transformations]], [[documentation:guide:symmetries_of_tensors]], [[documentation:guide:tensors_and_indices]],  [[documentation:guide:list_of_transformations]]
+  * Related transformations: [[documentation:ref:symmetrize]],  [[documentation:ref:fullyantisymmetrize]]